Approximating reals by sums of two rationals

JOURNAL OF NUMBER THEORY

卷:128

Article

Chan, Tsz Ho

关键词: Diophantine approximation;    character sum;    exponential sum;    Erdos-Turan inequality;   

DOI  :  10.1016/j.jnt.2007.06.011

来源: Elsevier

【 摘 要 】

We generalize Dirichlet's diophantine approximation theorem to approximating any real number alpha by a sum of two rational numbers a(1)/q(1) + a(2)/q(2) with denominators 1 <= q(1), q(2) <= N. This turns out to be related to the congruence equation problem xy =c (mod q) with 1 <= x, y <= q(1/2+is an element of). (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free